The paper presents the correlation and correlation coefficient of single-valued neutrosophic sets (SVNSs) based on the extension of the correlation of intuitionistic fuzzy sets and demonstrates that ...the cosine similarity measure is a special case of the correlation coefficient in SVNS. Then a decision-making method is proposed by the use of the weighted correlation coefficient or the weighted cosine similarity measure of SVNSs, in which the evaluation information for alternatives with respect to criteria is carried out by truth-membership degree, indeterminacy-membership degree, and falsity-membership degree under single-valued neutrosophic environment. We utilize the weighted correlation coefficient or the weighted cosine similarity measure between each alternative and the ideal alternative to rank the alternatives and to determine the best one(s). Finally, an illustrative example demonstrates the application of the proposed decision-making method.
A multicriteria fuzzy decision-making method based on weighted correlation coefficients using entropy weights is proposed under interval-valued intuitionistic fuzzy environment for the some ...situations where the information about criteria weights for alternatives is completely unknown. To determine the entropy weights with respect to a decision matrix provided as interval-valued intuitionistic fuzzy sets (IVIFSs), we propose two entropy measures for IVIFSs and establish an entropy weight model, which can be used to determine the criteria weights on alternatives, and then propose an evaluation formula of weighted correlation coefficient between an alternative and the ideal alternative. The alternatives can be ranked and the most desirable one(s) can be selected according to the values of the weighted correlation coefficients. Finally, two applied examples demonstrate the applicability and benefit of the proposed method: it is capable for handling the multicriteria fuzzy decision-making problems with completely unknown weights for criteria.
Water electrolysis is a promising source of hydrogen; however, technological challenges remain. Intensive efforts have focused on developing highly efficient and earth‐abundant electrocatalysts for ...water splitting. An effective strategy is proposed, using a bifunctional tubular cobalt perselenide nanosheet electrode, in which the sluggish oxygen evolution reaction is substituted with anodic hydrazine oxidation so as to assist energy‐efficient hydrogen production. Specifically, this electrode produces a current density of 10 mA cm−2 at −84 mV for hydrogen evolution and −17 mV for hydrazine oxidation in 1.0 m KOH and 0.5 m hydrazine electrolyte. An ultralow cell voltage of only 164 mV is required to generate a current density of 10 mA cm−2 for 14 hours of stable water electrolysis.
Sweet electrocatalytic synergy: An effective strategy for energy‐saving water electrolysis is presented. The sluggish oxygen evolution reaction is replaced by anodic hydrazine oxidation on a low‐cost and bifunctional cobalt perselenide electrode.
Arithmetic aggregation operators and geometric aggregation operators of intuitionistic fuzzy values (IFVs) are common aggregation operators in the fields of information fusion and decision making. ...However, their aggregated values imply some unreasonable results in some cases. To overcome the shortcomings, this paper proposes an intuitionistic fuzzy hybrid weighted arithmetic and geometric aggregation (IFHWAGA) operator and an intuitionistic fuzzy hybrid ordered weighted arithmetic and geometric aggregation (IFHOWAGA) operator and discusses their suitability by numerical examples. Then, we propose a multiple attribute decision-making method of mechanical design schemes based on the IFHWAGA or IFHOWAGA operator under an intuitionistic fuzzy environment. Finally, a decision-making problem regarding the mechanical design schemes of press machine is provided as a case to show the application of the proposed method.
In this work, considering the information carried by the membership degree and the non-membership degree in Atanassov’s intuitionistic fuzzy sets (IFSs) as a vector representation with the two ...elements, a cosine similarity measure and a weighted cosine similarity measure between IFSs are proposed based on the concept of the cosine similarity measure for fuzzy sets. To demonstrate the efficiency of the proposed cosine similarity measures, the existing similarity measures between IFSs are compared with the cosine similarity measure between IFSs by numerical examples. Finally, the cosine similarity measures are applied to pattern recognition and medical diagnosis.
► We propose an expected value method for intuitionistic trapezoidal fuzzy multicriteria decision-making problems, in which the preference values for an alternative on criteria and the weight values ...of criteria take the form of intuitionistic trapezoidal fuzzy numbers. ► We establish simple and exact formulas, which are derived to determine the expected weight values for criteria and the weighted expected values for alternatives. ► An illustrative example shows that the proposed method is simple and effective.
In this paper, we introduce the expected values for intuitionistic trapezoidal fuzzy numbers and presented a handling method for intuitionistic trapezoidal fuzzy multicriteria decision-making problems, in which the preference values of an alternative on criteria and the weight values of criteria take the form of intuitionistic trapezoidal fuzzy numbers. Simple and exact formulas are proposed to determine the expected weight values of the criteria for an alternative and weighted expected value for an alternative. Therefore, the expected value method is extended for ranking alternatives and the most desirable one(s) can be selected according to the weighted expected values. Finally, an illustrative example shows that the proposed method is simple and effective.
Clustering plays an important role in data mining, pattern recognition, and machine learning. Then, single-valued neutrosophic sets (SVNSs) are a useful means to describe and handle indeterminate and ...inconsistent information, which fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. To cluster the data represented by single-value neutrosophic information, the article proposes a single-valued neutrosophic minimum spanning tree (SVNMST) clustering algorithm. Firstly, we defined a generalized distance measure between SVNSs. Then, we present an SVNMST clustering algorithm for clustering single-value neutrosophic data based on the generalized distance measure of SVNSs. Finally, two illustrative examples are given to demonstrate the application and effectiveness of the developed approach.
On the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization ...of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine measure function of SVNHFSs. Also, we develop a single-valued neutrosophic hesitant fuzzy weighted averaging (SVNHFWA) operator and a single-valued neutrosophic hesitant fuzzy weighted geometric (SVNHFWG) operator and investigate their properties. Furthermore, a multiple-attribute decision-making method is established on the basis of the SVNHFWA and SVNHFWG operators and the cosine measure under a single-valued neutrosophic hesitant fuzzy environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.
A multicriteria fuzzy decision-making method based on weighted correlation coefficients using entropy weights is proposed under intuitionistic fuzzy environment for some situations where the ...information about criteria weights for alternatives is completely unknown. To determine the entropy weights with respect to a set of criteria represented by intuitionistic fuzzy sets (IFSs), we establish an entropy weight model, which can be used to get the criteria weights, and then propose an evaluation formula of weighted correlation coefficient between an alternative and the ideal alternative. The alternatives can be ranked and the most desirable one(s) can be selected according to the weighted correlation coefficients. Finally, two illustrative examples demonstrate the practicality and effectiveness of the proposed method.
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